A spatial stochastic frontier model including both frontier and error-based spatial cross-sectional dependence

Spatial dependence in stochastic frontier models is usually handled by modelling the frontier function or the inefficiency error term through the introduction of some spatial components. The model proposed in this paper (SDF-CSD) combines the two different modelling approaches, obtaining a full comprehensive specification that introduces four different sources of spatial cross-sectional dependence. The most appealing feature of the model is that it allows capturing global and local spatial spillover effects while controlling for spatial correlation related to firms' efficiency and to unobserved but spatially correlated variables. Moreover, it can be estimated using maximum likelihood techniques. Finally, some Monte Carlo simulations were run to test the final sample properties of the new spatial estimator and an application to the Italian agricultural sector is provided.